The displacement $y$ (in $cm$) in case of a simple harmonic wave is given by $y=\frac{10}{\pi} \sin \left(2000 \pi t-\frac{\pi x}{17}\right)$. The period and maximum velocity of the particles in the medium will respectively be

The equation of a wave is $Y = 6 \sin(12 \pi t - 0.02 \pi x + \frac{\pi}{3})$,where $x$ is in $m$ and $t$ is in $s$. The velocity of the wave is: (in $m/s$)

$A$ transverse wave on a string is described by $y = 3 \sin(36t + 0.018x + \pi/4)$,where $x$ and $y$ are in $cm$ and $t$ is in seconds. The least distance between two successive crests in the wave is . . . . . . $cm$. (Nearest integer) $(\pi = 3.14)$

The rope shown at an instant is carrying a wave travelling towards the right,created by a source vibrating at a frequency $n$. Consider the following statements:
$I.$ The speed of the wave is $4n \times ab$
$II.$ The medium at $a$ will be in the same phase as $d$ after $\frac{4}{3n} \text{ s}$
$III.$ The phase difference between $b$ and $e$ is $\frac{3\pi}{2}$
Which of these statements are correct?

The equation of a sound wave is $y = 0.0015 \sin (62.4 x + 316 t)$. Find the wavelength of this wave.

The equation of a travelling wave is given by $y = 0.5 \sin(20x - 400t)$,where $x$ and $y$ are in meters and $t$ is in seconds. The velocity of the wave is .... $m/s$.